use strict;
use warnings;

my ($lastline, $lastevent);
while (<DATA>) {
    chomp;
    next unless(/EVENT(\d)/);
    print "$lastline\n" if(defined($lastevent) and $1 ne $lastevent);
    $lastevent = $1;
    $lastline = $_;
}
print "$lastline\n";

__DATA__
09:12:50:861 EVENT1 #Don't want this line
09:13:09:467 EVENT1 #Don't want this line
09:13:09:837 EVENT1
09:13:38:059 EVENT2
09:14:03:115 EVENT3
09:14:04:076 EVENT4
09:14:11:376 EVENT1
09:14:34:049 EVENT2
09:14:34:990 EVENT3 #Don't want this line
09:14:34:990 EVENT3
09:14:34:990 EVENT4